Simplified T Model with Body Effect
Figure 1 shows the MOSFET T model with a Thévenin source in series with the gate and the
body connected to signal ground. We wish to solve for the equivalent circuit in which the sources
isg and isb are replaced by a single source which connects from the drain node to ground having
the value i0d = i0s . We call this the simplified T model. The first step is to look up into the branch
labeled i0s and form a Thévenin equivalent circuit. With i0s = 0, we can use voltage division to write
vs(oc) = vtg
vtg
rsb
rs /χ
= vtg
=
rs + rsb
rs + rs /χ
1+χ
(1)
With vtg = 0, the resistance rs0 seen looking up into the branch labeled i0s is
rs0 = rs krsb =
1
rs
=
1+χ
(1 + χ) gm
(2)
Figure 1: T model with Thévenin source connected to the gate and the body connected to signal
ground.
The simplified T model is shown in Fig.2. Compared to the corresponding circuit for the BJT,
the MOSFET circuit replaces vtb with vtg / (1 + χ) and re0 with rs0 = rs / (1 + χ). Because the gate
current is zero, set α = 1 and β = ∞ in converting any BJT formulas to corresponding MOSFET
formulas. The simplified T model is derived with the assumption that the body lead connects to
signal ground. In the case that the body lead connects to the source lead, it follows from Fig. 1
that isb = 0. Connecting the body to the source is equivalent to setting χ = 0 in the MOSFET
equations.
Figure 2: Simplified T model.
1